Nested loop: Pascal triangle

Problem: Print Pascal's triangle for a given n.

Example: n = 6


                  1 
                1    1 
             1    2    1 
           1    3    3    1 
        1    4    6    4    1 
     1    5   10   10    5    1 

Hint: An element in a given row is sum of adjacent elements in the previous row, example, 4 in row 5 is sum of 1 and 3 from row 4.

Solution in Python:


import math

def pascal_triangle(n):
    """
    Author: Mayur P Srivastava
    """

    row = []
    for i in range(n):
        new_row = []
        for j in range(i+1):
            col1 = j - 1
            col2 = j
            value = 0
            if col1 >= 0 and col1 < len(row):
                value += row[col1]
            if col2 >= 0 and col2 < len(row):
                value += row[col2]
            if value == 0:
                value = 1
            new_row.append(value)
        row = new_row

        print format_row(row, i+1, n)


def format_row(row, row_number, n, max_element_len=4):
    offset = int(math.floor((n - row_number) / 2))

    element_pattern = "%%%ds " % max_element_len

    row_str = ""
    for i in range(offset+1):
        row_str += element_pattern % ""

    for element in row:
        row_str += element_pattern % element

    return row_str



Concepts learned: Nested loops.